Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Author: Peter Tannenbaum
Publisher: PEARSON
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Chapter 13, Problem 63E
To determine
To find:
The dimensions of the rectangle from the given information.
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Students have asked these similar questions
==
1. A separable differential equation can be written in the form hy) = g(a) where h(y) is a function of y
only, and g(x) is a function of r only.
All of the equations below are separable. Rewrite each of these in the form h(y) = g(x), then find
a general solution by integrating both sides. Determine whether the solutions you found are explicit
(functions) or implicit (curves but not functions)
(a) 1' = — 1/3
(b) y' =
=
---
Y
(c) y = x(1+ y²)
Ja
дх
dx dx
Q3: Define the linear functional J: H()-R by
تاریخ
(v) = ½a(v, v) - (v)
==
Let u be the unique weak solution to a(u,v) = L(v) in H₁(2) and suppose that
a(...) is a symmetric bilinear form on H() prove that
a Buy v) =
1- u is minimizer. 2- u is unique. 3- The minimizer J(u,) can be rewritten under
J(u)=u' Au-ub,
algebraic form
Where A, b are repictively the stiffence matrix and the load vector
Q4: A) Answer only
1-show that thelation to
-Auf in N,
u = 0 on a satisfies the
stability Vulf and show that V(u-u,)||² = ||vu||2 - ||vu||2
lu-ulls Chu||2
2- Prove that
Where
=1
||ul|= a(u, u) = Vu. Vu dx + fu. uds
B) Consider the bilinear form
a(u, v) = (Au, Av) + (Vu, Vv) + (Vu, v) + (u, v)
Show that a(u, v) continues and V- elliptic on H(2)
(3)
(0.0), (3.0)
Q1: A) fill the following:
1- The number of triangular in a triangular region with 5 nodes is
quadrilateral with n=5 and m=6 nodés is
2- The complex shape function in 1-D
3- dim(P4(K))=-
(7M
--- and in the
and multiplex shape function in 2-D is
4- The trial space and test space for problem -Auf, u = go on and
B) Define the energy norm and prove that the solution u, defined by Galerkin
orthogonal satisfies the best approximation.
Q2: A) Find the varitional form for the problem
1330
(b(x)) - x²=0, 0
Chapter 13 Solutions
Excursions in Modern Mathematics (9th Edition)
Ch. 13 - Compute the value of each of the following. a. F15...Ch. 13 - Compute the value of each of the following. a. F16...Ch. 13 - Prob. 3ECh. 13 - Compute the value of each of the following. a....Ch. 13 - Describe in words what each of the expressions...Ch. 13 - Prob. 6ECh. 13 - Given that F36=14,930,352 and F37=24,157,817, a....Ch. 13 - Prob. 8ECh. 13 - Given that F36=14,930,352 and F37=24,157,817,...Ch. 13 - Given that F32=2,178,309 and F33=3,524,578, a.find...
Ch. 13 - Prob. 11ECh. 13 - Using a good calculator an online calculator if...Ch. 13 - Consider the following sequence of equations...Ch. 13 - Consider the following sequence of equations...Ch. 13 - Fact: If we make a list of any four consecutive...Ch. 13 - Fact: If we make a list of any 10 consecutive...Ch. 13 - Express each of the following as a single...Ch. 13 - Prob. 18ECh. 13 - Prob. 19ECh. 13 - Prob. 20ECh. 13 - Prob. 21ECh. 13 - Prob. 22ECh. 13 - Prob. 23ECh. 13 - Prob. 24ECh. 13 - Consider the quadratic equation x2=x+1. a. Use the...Ch. 13 - Prob. 26ECh. 13 - Consider the quadratic equation 3x2=8x+5. a. Use...Ch. 13 - Prob. 28ECh. 13 - Prob. 29ECh. 13 - Prob. 30ECh. 13 - Consider the quadratic equation 21x2=34x+55. a....Ch. 13 - Prob. 32ECh. 13 - Prob. 33ECh. 13 - Consider the quadratic equation (FN2)x2=(FN1)x+FN,...Ch. 13 - The reciprocal of =1+52 is the rational number...Ch. 13 - The square of the golden ratio is the irrational...Ch. 13 - Given that F4998.61710103, a. find an approximate...Ch. 13 - Prob. 38ECh. 13 - Prob. 39ECh. 13 - Prob. 40ECh. 13 - Prob. 41ECh. 13 - Prob. 42ECh. 13 - Triangles T and T shown in Fig. 13-23 are similar...Ch. 13 - Polygons P and P shown in Fig. 13-24 are similar...Ch. 13 - Find the value of x so that the shaded rectangle...Ch. 13 - Find the value of x so that the shaded figure in...Ch. 13 - Prob. 47ECh. 13 - Prob. 48ECh. 13 - Prob. 49ECh. 13 - Prob. 50ECh. 13 - In Fig. 13-31 triangles BCA is a 36-36-108...Ch. 13 - Prob. 52ECh. 13 - Find the value of x of y so that in Fig. 13-33 the...Ch. 13 - Prob. 54ECh. 13 - Prob. 55ECh. 13 - Consider the sequence of ratios FN2FN. a. Using a...Ch. 13 - Prob. 57ECh. 13 - Prob. 58ECh. 13 - Prob. 59ECh. 13 - a.Explain what happens to the values of (152)N as...Ch. 13 - Prob. 61ECh. 13 - Prob. 62ECh. 13 - Prob. 63ECh. 13 - Prob. 64ECh. 13 - Prob. 65ECh. 13 - Find the value of x of y so that in Fig. 13-37 the...Ch. 13 - Prob. 67ECh. 13 - In Fig. 13-39 triangle BCD is a 727236 triangle...Ch. 13 - Prob. 69ECh. 13 - Prob. 70ECh. 13 - Prob. 71ECh. 13 - Prob. 72ECh. 13 - Prob. 73ECh. 13 - Prob. 74ECh. 13 - Prob. 75ECh. 13 - Prob. 76ECh. 13 - During the time of the Greeks the star pentagram...
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